Things to know before attempting polynomial factorization ?

I have been learning things like these for some time now , i want to move to polynomial factorization

Prime Numbers

The first few prime numbers are 2, 3, 5, 7, 11, 13 .A prime number is a positive integer which has no factors other than 1 and itself. 1 itself, by definition, is not a prime number.Prime numbers cant be divided any further and thus can be thought of as the atoms of numbers.Any number which is not prime can be written as the product of prime numbers, we simply keep dividing it into more parts until all factors are prime

84 = 2 x 2 x 3 x 7

Prime Factor

A factor that is a prime number: one of the prime numbers that, when multiplied, give the original number.

Example: The prime factors of 15 are 3 and 5 (3×5=15, and 3 and 5 are prime numbers)

Greatest common factor (GCF)

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:List the prime factors of each number.Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Least common multiple (LCM)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Re: Things to know before attempting polynomial factorization ?

If {something} times {another_something} = {yet_another_something} then {something} and {another_something} are factors of {yet_another_something}

eg. We know that 2 x 6 = 12. 2 and 6 are factors of 12.

In your other post about primes we looked at lots of number factors. In your algebra book you are going to look at algebraic factors

... stuff like 2y + 6z = 2 times (y + 3z)

This started with two things added together and has landed up with two things multiplied together. That is what algebraic factorisation is about. You'll notice it is in part II. I think you need to do part I first. Then it'll be easier.

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo GalileiSometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

Re: Things to know before attempting polynomial factorization ?

I don't want to be discouraging but are you familiar with the expression "trying to run before you can walk" ?

We can get to that example eventually, but there's a lot to do first.

How much algebra have you done already? Please post an example of what you can do.

Bob

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo GalileiSometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

Re: Things to know before attempting polynomial factorization ?

hi tonyjaa,

There are two skills at work here: (1) having a pair of brackets and multiplying them to get a sum of terms and (2) reversing this by starting with the (quadratic) expression and putting it back into brackets as a pair of factors. I think it is easier to learn to do (1) before (2)

Only the correct choices above will give the correct middle term of 19x. I quickly try out all the combinations to see which works.

Bob

ps. You'll notice I wrote 'times' rather than use a cross: 'x'. Unfortunately mathematicians like using 'x' for an unknown amount, and also as the multiplication sign. This could lead to confusion. So in algebraic expressions the multiply sign is often left out completely. This is why 2 times x is written as 2x. No times sign at all.

And 6 times x times x is written as 6x² (say: six ex squared)

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo GalileiSometimes I deliberately make mistakes, just to test you! …………….Bob Bundy